Chickens will not moan out of pain. That would simply attract predators.
How has she been acting otherwise?
Has she been running around like normal?
Eating and drinking?
Clucking or making any other sounds?
Panting as if she is hot?
Has she been making this sound nonstop?

That sound is called stridor, and it may be that she has something--an object or piece of food--stuck in her airway. I would get an extra pair of hands and look inside her throat for any object or unusual looking yellow or white patches. Many people have posted here about similar sounds from a hen that disappeared overnight. Here is a link about stridor: http://www.merckmanuals.com/profess.../symptoms_of_pulmonary_disorders/stridor.html

Yeah, that is the only thing that came to mind for me too. However, it doesn't sound like a rasping or wheezing type of moan.
Maybe if she is acting normal otherwise, it is just one of those quirky chicken things?

According to The Children and my wife she was fine until about 5pm (EDT) Then she started doing what is in the video. She just stands in one spot. Basically what is in the video is all she is doing. We will try to get in her throat so see if there is anything in there. She and the others were out running free in the yard. Nothing has changed out there. and the tend to stay together. All the others are fine.